In this paper, we investigate the mean change-point models based on associated sequences. Under some weak conditions, we obtain a limit distribution of CUSUM statistic which can be used to judge the mean change-mount ${\delta }_n$ is satisfied or dissatisfied $n^{1/2}{\delta }_n=o\left(1\right)$. We also study the consistency of sample covariances and change-point location statistics. Based on Normality and Lognormality data, some simulations such as empirical sizes, empirical powers and convergence are presented to test our results. As an important application, we use CUSUM statistics to do the mean change-point analysis for a financial series.

中文翻译：

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基于依赖序列的变点模型的CUSUM统计

在本文中，我们研究了基于关联序列的平均变化点模型。在一些弱条件下，我们得到了一个 CUSUM 统计量的极限分布，可以用来判断平均变化量${\delta }_n$满意或不满意$n^{1/2}{\delta }_n=○\left(1\right)$. 我们还研究了样本协方差和变化点位置统计的一致性。基于正态性和对数正态性数据，提出了一些模拟，如经验大小、经验幂和收敛性来测试我们的结果。作为一个重要的应用，我们使用 CUSUM 统计对金融序列进行平均变点分析。